Question

Question 3 options:

The owner of the Britten's Egg Farm wants to estimate the mean number of eggs produced per chicken.  A representative random sample of 20 chickens show they produce an average of 25 eggs per month with a sample standard deviation (s) of 2 eggs per month. The distribution is known to be symmetrical and is close enough to normal to be treated as a normal distribution.

Answer the following questions related to the above paragraph and then calculate a 90% confidence interval for the mean number of eggs produced per chicken on the Britten's Egg Farm.

A What is the point estimate of the mean number of eggs produced per chicken?
       Enter answer with 0 decimal places (integer).

B Calculate the margin of error for the 90% confidence interval for the mean amount of eggs laid per month on the Britten's Egg Farm.

Enter answer rounded to 1 decimal point.
Include a zero to the left of the decimal point if the margin of error is a number between -1 and +1.

c The 90% conference interval for the mean number eggs produced per month is:

Enter the lower and upper limits for the conference interval by entering the lower limit first.
Rounded each conference limit to 1 decimal point.

D Prior to this study the owner of the Britten's Egg Farm Egg Farm believed the mean amount off eggs produced per month on his farm was 30.

Does the study support his belief with a 90% confidence?

a     Yes. The mean amount of eggs produced per month on his farm could be 30 per month because the number 30 is not contained in the confidence interval.

b     Yes. The mean amount of eggs produced per month on his farm could be 30 per month because the number 30 is contained in the confidence interval.

c     No. The mean amount of eggs produced per month on his farm is most likely not 30 per month because the number 30 is not contained in the confidence interval.

d     No. The mean amount of eggs produced per month on his farm is most likely not 30 per month because the number 30 is contained in the confidence interval.

e    The owner can not comment on the mean amount of eggs produced per month on his farm because the confidence interval is based upon a sample.

Answer 1

Solution:

Given: A representative random sample of 20 chickens show they produce an average of 25 eggs per month with a sample standard deviation (s) of 2 eggs per month.

The distribution is known to be symmetrical and is close enough to normal to be treated as a normal distribution.

Thus

Sample Size = n = 20

Sample Mean =

Sample Standard Deviation = s = 2

Part A) What is the point estimate of the mean number of eggs produced per chicken?

Sample Mean is an unbiased estimator of population mean, thus point estimate of the mean number of eggs produced per chicken is:

Part B) Calculate the margin of error for the 90% confidence interval for the mean amount of eggs laid per month on the Britten's Egg Farm.

c = confidence level = 90% = 0.90

Margin of Error is given by:

where t_c is t critical value.

df = n - 1 = 20 - 1 = 19

Two tail area = 1 - c = 1 - 0.90 = 0.10

t_c = 1.729

Part C) The 90% conference interval for the mean number eggs produced per month is:

Formula:

Lower Limit = 24.2

Upper Limit = 25.8

Part D)  Prior to this study the owner of the Britten's Egg Farm Egg Farm believed the mean amount off eggs produced per month on his farm was 30.

Does the study support his belief with a 90% confidence?

Since 90% confidence interval is which does not include Number of eggs per month=30.

Thus correct option is:

c     No. The mean amount of eggs produced per month on his farm is most likely not 30 per month because the number 30 is not contained in the confidence interval.